Nuprl Lemma : face-zero-and-one
ā[X:jā¢]. ā[z:{X ā¢ _:š}]. (((z=0) ā§ (z=1)) = 0(š½) ā {X ā¢ _:š½})
Proof
Definitions occuring in Statement :
face-zero: (i=0)
,
face-one: (i=1)
,
face-and: (a ā§ b)
,
face-0: 0(š½)
,
face-type: š½
,
interval-type: š
,
cubical-term: {X ā¢ _:A}
,
cubical_set: CubicalSet
,
uall: ā[x:A]. B[x]
,
equal: s = t ā T
Definitions unfolded in proof :
uall: ā[x:A]. B[x]
,
member: t ā T
,
squash: āT
,
true: True
,
subtype_rel: A ār B
,
uimplies: b supposing a
,
guard: {T}
,
iff: P
āā Q
,
and: P ā§ Q
,
rev_implies: P
ā Q
,
implies: P
ā Q
Lemmas referenced :
equal_wf,
cubical-term_wf,
face-type_wf,
face-and-com,
face-zero_wf,
face-one_wf,
face-0_wf,
iff_weakening_equal,
face-one-and-zero,
interval-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
applyEquality,
thin,
instantiate,
lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
because_Cache,
hypothesis,
hypothesisEquality,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination,
independent_functionElimination,
universeIsType,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[z:\{X \mvdash{} \_:\mBbbI{}\}]. (((z=0) \mwedge{} (z=1)) = 0(\mBbbF{}))
Date html generated:
2020_05_20-PM-02_43_24
Last ObjectModification:
2020_04_04-PM-04_57_39
Theory : cubical!type!theory
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